SOLUTION: A model rocket is launched from a platform. The trajectory of the rocket can be modelled by the relation h=−5t^2+100 t+15, where h is the height of the model rocket in meters a

Question 1199344: A model rocket is launched from a platform. The trajectory of the
rocket can be modelled by the relation h=−5t^2+100 t+15, where h is the
height of the model rocket in meters and t is the time in seconds.
a) What is the height of the platform?
b) What is the height of the model rocket after 4 seconds?
c) What is the maximum height reached by the rocket? How long does
it take to reach this height?
d) Approximately how long is the rocket in the air?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the equation is h = 5^2 + 100t + 15.
h is the height of the rocket.
t is the time in seconds.

the height of the platform is the height when t = 0 which is 15 meters high.

the height of the rocket after 4 seconds is found by replacing t with 4 and solving for h.
you get h = -5 * 4^2 + 100 * 4 + 15 = 335 meters.

the maximum height reached by the rocket is when t = -b/2a.

a = the coefficient of the t^2 term = -5
b is the coefficient of the t term = 100
c is the constant term = 15

t = -b/2a becomes t = -100 / -10 = 10
when t = 10, h = -5 * 10^2 + 100 * 10 + 15 = 515 meters.

it takes 10 seconds for the rocket to reach the maximum height.

the equation can be graphed by letting y represent h and x represent t.
here's what the graph looks like.

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up

    - Introductory lesson on a projectile thrown-shot-launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform

Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn on how to solve this type of problems once and for all.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

RELATED QUESTIONS
A toy rocket is launched in an open field. The path of the rocket can be modelled by the... (answered by ikleyn)
A model rocket is launched straight upward with an initial velocity of 22m/s. The height... (answered by Alan3354)
A rocket is launched straight upwards with an initial velocity of 80 m/s. The height of... (answered by ikleyn)
A model rocket launched straight upward with an initial velocity of 200 m/s. The height... (answered by scott8148)
A model rocket is launched from a platform and its height h metres is given as a function (answered by Alan3354)
A model rocket is launched straight up from a platform. The height of the rocket is given (answered by scott8148)
A model rocket is launched from the roof of a building. It's flight path is b modeled by... (answered by Boreal)
A toy rocket is launched from a platform that is 4 feet above the ground. The height, h,... (answered by CharlesG2)
A model rocket is launched off the top of a platform. The height of the rocket is given... (answered by galactus)